Sampling of analog signals in order to enable digital signal processing is used in a wide variety of applications and for various signal types. Numerous sampling schemes are known in the art, some of which attempt to reduce the sampling rate while ensuring that the digital samples represent the analog signal with high accuracy. The well-known Shannon-Nyquist theorem, for example, states that a general band-limited signal should be sampled at twice its highest frequency in order to enable perfect reconstruction.
Some sampling schemes attempt to exploit certain signal characteristics in order to reduce the sampling rate below the Nyquist rate. For example, some analog signals can be characterized as having a finite number of degrees of freedom per unit time, also referred to as a Finite Rate of Innovation (FRI). One example of an FRI signal is a stream of analog pulses. Reception and reconstruction of analog pulse sequences are performed, for example, in ultrasound imaging and other medical imaging, processing of neuronal signals, image processing, radar systems and Ultra-Wideband (UWB) communication.
Example schemes for sampling FRI signals such as pulse sequences have been proposed by Vetterly et al., in “Sampling Signals with Finite Rate of Innovation,” IEEE Transactions on Signal Processing, volume 50, no. 6, June, 2002, pages 1417-1428; and by Blu et al., in “Sparse Sampling of Signal Innovations,” IEEE Signal Processing Magazine, volume 25, no. 2, March, 2008, pages 31-40, which are incorporated herein by reference.
Other examples of sampling FRI signals are described by Maravic and Vetterli, in “Sampling and Reconstruction of Signals with Finite Rate of Innovation in the Presence of Noise,” IEEE Transactions on Signal Processing, volume 53, no. 8, August, 2005, pages 2788-2805; by Dragotti et al., in “Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang-Fix,” IEEE Transactions on Signal Processing, volume 55, no. 5, May, 2007, pages 1741-1757; and by Seelamantule and Unser, in “A Generalized Sampling Method for Finite-Rate-of-Innovation-Signal Reconstruction,” IEEE Signal Processing Letters, volume 15, 2008, pages 813-816, which are all incorporated herein by reference.
Some signal sampling schemes use multi-channel configurations. Multi-channel sampling schemes are described, for example, by Kusuma and Goyal, in “Multichannel Sampling of Parametric Signals with a Successive Approximation Property,” IEEE International Conference on Image Processing, Atlanta, Ga., October, 2006, pages 1265-1268; and by Olkkonen and Olkkonen, in “Measurement and Reconstruction of Impulse train by Parallel Exponential Filters,” IEEE Signal Processing Letters, volume 15, 2008, pages 241-244, which are incorporated herein by reference.